Conventional stereograms are pictures or illustrations which are formed on a page or screen in black and white, or in color. The underlying pattern of the stereogram, prior to creating raised or lowered images, is referred to as the base art or base stereogram. In a stereogram the base art consists of a series of adjoining, repeating bands. In the case of a random dot stereogram, the repeating bands are comprised of randomly generated picture elements (pixels). Each band has the same width (in the horizontal direction), and preferably the same height (in the vertical direction).
Upon examination by a viewer who fixes his focus on the stereogram in a prescribed manner, the stereogram appears to contain three-dimensional (3-D) images. That is, there is at least one three-dimensional image embedded in the stereogram, and certain portions of that embedded image appear to be raised or higher relative to the plane of the screen or paper. In addition or in the alternative, other images in other portions of the illustration may appear recessed or lowered. The term "image" when used herein means the 3-D impression in the stereogram.
In order to view the stereogram, the observer should focus on a point behind the stereogram and then move his eyes to focus on the stereogram itself. Or the observer should hold the stereogram close to his nose so that it appears blurry, then relax and stare and attempt to look "through" the stereogram. Then he should slowly move the stereogram away from his face until three-dimensional images appear.
A stereogram operates on the principle that, when looking straight ahead at an object, a person's left eye sees a slightly different view of the object than his right eye. A person's perception of depth is provided by these two slightly different views or perspectives of the same object. When the object is placed closer to the viewer, his eyes are forced to cross somewhat to focus on the object. His eyes interpret this crossing as meaning that the object is nearer or "raised". Thus, a stereogram gives the illusion of depth by providing two slightly offset images. When the left eye focuses on one such image and the right eye focuses on the other image, the result is an apparent difference in the relative depth of the two images. Alternatively, some viewers may cross their eyes in front of the stereogram to view the image.
Thus, a stereogram operates on the principle that the eyes can be fooled into perceiving an illusion of three-dimensions by creating one image on which the left eye focuses, and a slightly offset image on which the right eye focuses. The offset or shift in position between the two images, combined with an altered band width in the region of the shift, creates the illusion of 3-D.
Many people are familiar with stereoscopic art forms such as 3-D movies or stereoscopic viewers. Both of these forms require lenses to be placed over the eyes to achieve the desired depth perception. In the case of 3-D movies, a red lens and a green lens over the eyes permit one eye to view a red image on the screen while the other eye views a green image. The two colored images are positioned somewhat differently relative to the viewing background to give the illusion of depth.
There are also stereograms, however, which do not require any lenses or any other assistance to view them. Sometimes this type of stereogram is referred to a bare-eyed stereogram. The instant invention is concerned with bare-eyed stereograms.
A bare-eyed stereogram is created by arranging repeating vertical bands of artwork having a characteristic repetition width along a horizontal line. These repeating bands form the base art of the stereogram. The 3-D height effect or "rise" is created by shifting a portion of the base art to the left or the right. It is immaterial whether the direction of shift is toward the left along the horizontal line, or to the right. Horizontal here is defined as parallel to the line between the observer's eyes. However, consistency along the horizontal line and neighboring horizontal lines must be maintained in terms of further shifts. For example, a leftward shift to signify a raise in the height of the image, must be maintained. The choice of direction is, therefore, arbitrary and may merely depend on where the design is intended to have the greatest amount of distortion, because the level of distortion increases in the direction opposite to the direction of shift. For the instant invention, the convention that has been chosen is that a leftward shift corresponds to a rise in the height of the shifted image.
The material selected for raising or lowering can be a geometric shape, letter or any other desired shape. The shape of any such form can be approximated by a collection of small flat sections, provided that such sections are sufficiently small. As explained below, it is necessary to decrease (increase) the repetition width of the raised (lowered) portion by an amount equal to the amount of the shift. Although in this general discussion, the shift and the change in repeat width are treated as separate items, it is actually the change in repeat width that causes an appearance of a shift.
In effecting a rise in the level of a flat shape, the shape is shifted leftward so that a portion of the adjacent band to the left of the selected band will be covered by the shifted shape. It is actually the reduction in the repeat width of the shape that causes the appearance of a shift. At the rightmost edge of the shifted shape a dislocation or gap will appear in the original art from which the shape was shifted. In order to maintain the appearance of the stereogram, the dislocation must be filled. The dislocation should be filled with additional artwork which is different in design and color than the base stereogram pattern because the region of the dislocation is intended to be at a lower level than the "raised" portion so that the illusion is that one sees "behind" the raised shape. It is also necessary to resume the original repetition width of the base art (i.e., the original width of the band) to the right of the raised section, if it is desired that this region to the right be at the base level.
When the repetition width of the raised section is reduced, an observer viewing adjacent bands near that image will find that his eyes become somewhat more crossed and his eyes are thus fooled into believing that the narrower portion is closer or raised relative to the wider repetition width portions. Conversely, a rightward shift and increase in the repeat width involves a lowering of the shape. The final stereogram may contain a plurality of such raised or lowered portions within the same image.
Until now, known bare-eyed stereograms were of the type known as random dot stereograms. Random dot stereograms are stereograms formed from bands of randomly generated black and white (or colored) picture elements (pixels). A picture element is a contiguous region of a continuous tone artwork having a definite boundary. A pixel is the special case of a picture element which is square and is arranged in rows and columns and has an associated color. These pixels are small rectangular blocks or cells which can be represented on a computer screen and are manipulated by known electronic processing and imaging techniques. Pixel-based representations, regardless of the size of the pixel cells, are also known as raster-based representations if the stereogram is created, displayed or otherwise formed by such a representation.
Random dot stereograms are thus particularly well suited to computer image processing techniques. The pixels contained in random dot stereograms are relatively large and are visible to the eye. There are smaller pixels, called micropixels, which are well suited to the representation of continuous tone artwork. Such micropixels are typically a factor of ten or more smaller than the pixels used in random dot stereograms. The method contained herein involves associating each micropixel with a particular location along the x axis and the y axis of the screen or display, as well as associating each micropixel with a color level, for example an RGB color level, and with a value indicating the depth level at that pixel. In situations where stereograms are to be superimposed, transparency information must also be associated with each pixel.
Stereograms are useful as games and as means for encoding a message or graphical representation within a seemingly flat design. They can also be used as instructional aids in demonstrating how depth perception is detected by the eye. Some individuals can observe three-dimensional images in stereograms quickly, others may need much practice and still others may be unable to see the images.
Unlike the random dot stereograms, the methods and stereograms described herein are formed from repeating vertical strips of continuous tone artwork. It is convenient to represent such artwork in raster form at a micropixel level. However, the methods described do not depend upon the use of such raster-based artwork, and can be applied to vector-based and manual image processing techniques as well.
Further discussion of single image random dot stereograms is provided in a November 1991 article in Omni magazine by Scot Morris. The Omni article discusses the need to shift the dots to obtain the desired 3-D image. N. E. Thing Enterprises at One Kendall Square, Building 200, Cambridge, Mass. 02139, has also published stereograms and marketed software suitable for stereogram generation entitled Stare-EO Workshop, written and produced by Micro Synectic, Inc. This program creates random dot stereograms which contain various colors. Each color in the drawing (16 different colors are possible) represents a level of elevation of the stereogram image, either recessed into or out of the screen (or flat). In addition, Ultra Grafix Co. of Arlington, Tex., and NVision Grafix, Inc. of Dallas, Tex., and Front Line Art Publishing of San Diego, Calif. have marketed stereogram posters.
Random dot stereograms are constructed from base art consisting of repeated patterns of black and white random dots. The most obvious disadvantage of random dot stereograms is that the black and white dots are unattractive and unappealing to the eye and it would be much more aesthetically pleasing to produce a stereogram based on continuous tone (especially colored) artwork. The term color value used herein refers also to black and white stereograms. But there is another major disadvantage of random dot stereograms. The number of levels of the images embedded in the stereogram is limited because the width of the picture element cell is the smallest amount by which a shift can be made. Since the shifts produce depth, it is impossible to obtain a smoothly slowly varying curved surface with random dot stereograms which make use of relatively large pixels. Three dimensional objects that have continuous variation in depth can certainly be represented as random dot stereograms. However, the appearance of the image of the object is jagged and bumpy.
Three-dimensional images in continuous tone stereograms avoid this problem of jaggedness and, coupled with the beauty of full color artwork, they result in a major improvement to the black and white random dot stereogram.
An article by G. Slinker and R. Burton in the Journal of Imaging Science and Technology, Volume 36, No. 3, May/June 1992, shows that a random dot stereogram image can be generated by a series of patterned bands having a certain repetition rate (width). Each picture element in the image is associated with a depth level. By shifting a portion of the pattern a depth perception can be obtained. There is no disclosure of stereograms based on continuous tone artwork, nor is there any disclosure of a method to fill the gaps left by changing repeat widths.
Another discussion of random dot stereograms appears in a book entitled Random Dot Stereograms, published by Kinsman Physics, 1992, by Andrew A. Kinsman. Once again there is no disclosure of stereograms based upon continuous tone artwork nor is there disclosure of any technique of filling the gaps by other than randomly generated pixels.
Thus, the prior art random dot stereograms contain certain fundamental features: (1) producing a strip of base art consisting of random black and white or colored cells arranged in a rectangular shape and then repeating this rectangular shape at regular horizontal intervals side by side to create the repetitive base art; (2) creating depth information for each pixel of the base art. If the depth information is inputted by means of an equation, creating depth information is extremely simple, but if the depth information is inputted using other techniques then such programs would require some form of inputting technique or user interface; (3) interpreting the depth information to arrive at a new color or black/white value for each pixel in the base art.
The most convenient way to perform this process is to process each horizontal line separately and to determine for each pixel on the line which color value it should have. Such a determination depends on the color values of the pixels to the right (or to the left) and also on the amount of depth assigned to that particular pixel. Starting at some point on the horizontal line and moving in a given direction (for example, starting on the left and moving to the right) the depth will vary up or down as compared with the previous pixel. If the variation of depth is upward (i.e., a raise) for a given pixel as compared with the previous pixel, then the determination of the color value for that new pixel can simply be made by computing a new repeat width for that particular pixel which is given by the original repeat width of the base art minus an additional amount proportional to the amount of change in depth at that particular pixel. This new repeat width is maintained with regard to the next pixel unless there is a subsequent change in depth on that pixel as well. For example, if a flat area is raised and the pixels are processed from the left, a new repeat width is calculated for the first pixel in the raised area and then that repeat width is assigned to all subsequent pixels to the right unless they change in depth. In other words, it is the change in depth that determines the amount of the repeat width.
For example, for a surface having a depth characteristic that rises continuously from left to right, the repeat width would continuously decrease as one moves from pixel to pixel from the left to the right. However, for changes in levels that represent a lowering (recession) from the previous pixel, additional factors must be considered. First of all, for every recessive displacement or lowering, a "gap" is created which must be filled with additional artwork, i.e., with a new pattern of pixels different from the colored patterns of the pixels in the base art. In the case of random dot stereograms supplying additional artwork can easily be accomplished by randomly generating the color values for these pixels appearing in the "gap", just as the original base art strip was created by randomly assigning black and white values to each pixel.
In addition to the gap that appears when there is a recession, there is also an increase in the repeat width which is proportional to the amount of recessive displacement in depth from a given pixel to next pixel. This increase in repeat width for recessive displacements does not have any effect across the width of the gap but after the gap is generated, the new value for the repeat width takes effect at subsequent pixels appearing at the edge of the gap and beyond.
In order to produce a smoother variation of depth than heretofore attainable in random dot stereograms, it is not possible to simply decrease the size of the dots in random dot stereograms because, beyond a certain minimum size, the eye has difficulty distinguishing individual dots and the dots will blur into one continuous gray or other color tone. If your eye cannot distinguish individual dots, then the ability of the stereogram to encode depth fails since the eye will not be able to see changes in repeat widths on the final art.
The actual limit on the size of the dot for random dot stereograms depends to some extent on a given person's eyesight. However, as the dots get smaller than a thirtieth of an inch, the eye has trouble seeing the effects of the stereogram. In other words, the larger the dot, the easier it is for your eye to see the stereogram but the "bumpier" the 3-D image appears. As the dots get smaller and smaller, your eye has much more difficulty seeing a stereogram even though the smoothness of the stereogram improves.
In another aspect of bare-eyed stereograms, the method of creating a stereogram by spacing objects evenly in rows whereby one row has equal spacing between objects and the next row has different spacing between objects has been known. For example, N. E. Thing Enterprises makes some postcards which show this. The stepping procedure of the invention is an improvement whereby the objects in a given row appear at different levels from other objects in the same row. Also, a combination of superimposition of multiple stereograms and stepping creates an improved stereogram.
Continuous tone stereograms are a major improvement over random dot stereograms because they are more attractive than the random dot stereograms and they also provide for a more continuous variation of depth.
Stereograms which are available currently are designed for viewing from a relatively close distance, i.e., up to about 1-6 feet away. However, stereograms that are viewed at this distance are limited to viewing by a few observers at a time. Such stereograms would be unavailable for use in mass advertising such as billboards, or in a movie theater in a moving picture illustration.
Also, it has not been known to superimpose stereograms having transparency information, nor has a stepping procedure for producing stereograms been known.
In summary, no method is known to produce continuous tone art based stereograms which have satisfactory method to fill gaps or dislocations that result when portions of the artwork are shifted. Also, known stereograms are ill-suited to viewing on a large screen or by a mass audience.